Calculating the risk of system failure in a heterogeneous distributed network

Background
Degoo is developing a P2P Backup system which has its roots in the Master’s Thesis “CollabBackup: A Peer-to-Peer backup system focused on storage efficiency”. There’s still some work needed before the system is ready for the commercial market. This Master’s Thesis is an important part of that.

Description
The goal of the thesis is to investigate and implement a mathematical model which calculates the risk of system failure in a distributed system with heterogeneous nodes. The system is considered available when at least b of the rb nodes are available (where r is the replication-factor and b is an arbitrary integer). The easiest way to model this is using a binomial distribution. Unfortunately this model assumes that the nodes are independent and have the same availability. If you cannot assume that the model quickly becomes a lot more complex to implement and the time complexity of many of the solutions makes them unusable. The goal of this thesis is therefore to:

*Investigate and implement a model which has better accuracy than the cumulative binomial distribution function but is fast enough to be used in a system with millions of nodes.
*Implement the server-side code which handles resource allocations based on the model.
*Write the final report.